The ratio of the forces between two small spheres with constant charge $(a)$ in air and $(b)$ in a medium of dielectric constant $K$ is:

Two charges $q$ and $-3q$ are placed fixed on the $x$-axis separated by a distance $d$. Where should a third charge $2q$ be placed such that it will not experience any force?

$A$ point charge $Q$ is placed at the center of the line joining two equal point charges $+q$ and $+q$. The value of $Q$ if the system of the charges is in equilibrium,is

Two charges each of charge $+10 \mu C$ are kept on $Y$-axis at $y=-a$ and $y=+a$, respectively. Another point charge $-20 \mu C$ is placed at the origin and given a small displacement $x$ $(x \ll a)$ along $X$-axis. The force acting on the point charge is ($x$ and $a$ are in metres, $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$)

Three charges $+5 q, Q$ and $-2 q$ are kept along a straight line in the same order such that $+5 q$ and $-2 q$ charges are at a distance of $\frac{2 r}{3}$ and $\frac{r}{3}$ from the charge $Q$ respectively. If the net force on the charge $-2 q$ is zero,then $Q$ is

Three charges are placed as shown in the figure. The magnitude of $q_1$ is $2.00\, \mu C$,but its sign and the value of the charge $q_2$ are not known. Charge $q_3$ is $+4.00\, \mu C$,and the net force on $q_3$ is entirely in the negative $x-$ direction. The magnitude of $q_2$ is